More particularly, the invention relates to a controllable hydraulic vibration-damping support intended to be interposed for damping purposes between first and second rigid elements, said vibration-damping support comprising:                first and second strength members adapted to be secured to two rigid elements to be connected together,        an elastomer body which connects the first and second strength members and which delimits, at least in part, a working chamber,        a deformable compensation chamber which communicates with the working chamber via a first constricted passageway, the compensation chamber, working chamber, and first constricted passageway forming a hydraulic volume filled with liquid, the first constricted passageway having a resonance frequency of between 5 and 20 Hz,        an auxiliary chamber,        a decoupling valve comprising: an elastomeric isolating diaphragm which separates the working chamber and the auxiliary chamber; and first and second stop gates respectively communicating with the working chamber and with the auxiliary chamber, the isolating diaphragm being arranged between the first and second stop gates and distanced from each stop gate to allow it to travel freely between said first and second stop gates,        a control device adapted for selectively locking the isolating diaphragm.        
Document EP-A-0115417 discloses a vibration-damping support of this type, where the auxiliary chamber is a pneumatic chamber and the control device can selectively isolate or connect this auxiliary chamber to the open air.
The object of the present invention is to improve the effectiveness of vibration-damping supports of this type.